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Minimal identities of octonion algebras
On montre que des octonions sur un corps de caracteristique non 2, 3 ou 5 ne satisfont pas d'identite polynomiale de degre 4 et que les identites de degre 5 sont toutes obtenues a partir de deuxExpand
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Primitive Superalgebras with Superinvolution
Abstract Our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras [ 5 , 6 , 10 ] and to classify primitive superrings withExpand
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On maximal subalgebras
Let F be a field and &’ a unital (not necessarily associative) algebra over F. Our purpose is to determine the proper subalgebras of &’ which are maximal with respect to inclusion. This is done forExpand
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Springer forms and the first Tits construction of exceptional Jordan division algebras
In this paper, a certain quadratic form, originally due to Springer [15], which may be associated with any separable cubic subfield living inside an exceptional simple Jordan algebra is related toExpand
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Jordan rings with nonzero socle
Let Jbe a nondegenerate Jordan algebra over a commutative associative ring $ containing j. Defining the socle @ of \ to be the sum of all minimal inner ideals of J, we prove that @ is the direct sumExpand
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Maximal subalgebras of central separable algebras
Let A be a central separable algebra over a commutative ring R. A proper R-subalgebra of A is said to be maximal if it is maximal with respect to inclusion. THEOREM. Any proper subalgebra of A isExpand
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A simple proof of a theorem of Albert
A simple proof is given of the following theorem of Albert: An associative division algebra of degree 4 over its center is of order 4 in the Brauer group if and only if it cannot be written as aExpand
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Minimal identities of symmetric matrices
Let Hn (F) denote the subspace of symmetric matrices of Mn (F), the full matrix algebra with coefficients in a field F . The subspace Hn (F) c Mn (F) does not have any polynomial identity of degreeExpand
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